Integral formulation of Dirac singular waveguides
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917407416647680 |
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| author | Bal, Guillaume Hoskins, Jeremy Quinn, Solomon Rachh, Manas |
| author_facet | Bal, Guillaume Hoskins, Jeremy Quinn, Solomon Rachh, Manas |
| contents | This paper concerns a boundary integral formulation for the two-dimensional massive Dirac equation. The mass term is assumed to jump across a one-dimensional interface, which models a transition between two insulating materials. This jump induces surface waves that propagate outward along the interface but decay exponentially in the transverse direction. After providing a derivation of our integral equation, we prove that it has a unique solution for almost all choices of parameters using holomorphic perturbation theory. We then extend these results to a Dirac equation with two interfaces. Finally, we implement a fast numerical method for solving our boundary integral equations and present several numerical examples of solutions and scattering effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Integral formulation of Dirac singular waveguides Bal, Guillaume Hoskins, Jeremy Quinn, Solomon Rachh, Manas Mathematical Physics Numerical Analysis Analysis of PDEs This paper concerns a boundary integral formulation for the two-dimensional massive Dirac equation. The mass term is assumed to jump across a one-dimensional interface, which models a transition between two insulating materials. This jump induces surface waves that propagate outward along the interface but decay exponentially in the transverse direction. After providing a derivation of our integral equation, we prove that it has a unique solution for almost all choices of parameters using holomorphic perturbation theory. We then extend these results to a Dirac equation with two interfaces. Finally, we implement a fast numerical method for solving our boundary integral equations and present several numerical examples of solutions and scattering effects. |
| title | Integral formulation of Dirac singular waveguides |
| topic | Mathematical Physics Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2312.16701 |